Peaks, Valleys, and Blur: Optimization and Uncertainty Quantification - presented by Prof. Harry Dankowicz

Peaks, Valleys, and Blur: Optimization and Uncertainty Quantification

Prof. Harry Dankowicz

Prof. Harry Dankowicz

Associated Nonlinear Dynamics article

Z. Ahsan et al. (2022) Methods of continuation and their implementation in the COCO software platform with application to delay differential equations. Nonlinear Dynamics
Article of record
Peaks, Valleys, and Blur: Optimization and Uncertainty Quantification
Prof. Harry Dankowicz
Harry Dankowicz
University of Maryland, College Park

I describe the integration of parameter continuation techniques with variational calculus and covariance analysis for purposes of design optimization and uncertainty quantification along families of periodic and quasi-periodic orbits of nonlinear dynamical systems, as well as solutions to more general classes of multi-segment boundary-value problems, including those coupled through time delays. This integration has been realized in the Matlab-based software package COCO by supporting the automated construction of adjoint contributions to the corresponding Karush-Kuhn-Tucker conditions. I describe the general software design principles and illustrate the methodology on toy problems that capture the full complexity of the approach while also allowing for analytical and/or simulation-based validation.

References
  • 1.
    Z. Ahsan et al. (2019) Optimization along families of periodic and quasiperiodic orbits in dynamical systems with delay. Nonlinear Dynamics
  • 2.
    Z. Ahsan et al. (2022) Methods of continuation and their implementation in the COCO software platform with application to delay differential equations. Nonlinear Dynamics
  • 3.
    H. Dankowicz and J. Sieber (2022) Sensitivity analysis for periodic orbits and quasiperiodic invariant tori using the adjoint method. Journal of Computational Dynamics
  • 4.
    https://doi.org/10.48550/arXiv.2404.13429
Grants
    Engineering and Physical Sciences Research CouncilEP/N023544/1Engineering and Physical Sciences Research CouncilEP/V04687X/1
Nonlinear Dynamics, an International Journal of Nonlinear Dynamics and Chaos in Engineering Systems logo
Nonlinear Dynamics
Nonlinear Dynamics, an International Journal of Nonlinear Dynamics and Chaos in Engineering Systems
Cite as
H. Dankowicz (2024, May 9), Peaks, Valleys, and Blur: Optimization and Uncertainty Quantification
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